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Let b, c be positive integers, x 1 , x 2 be indeterminates over Z and x m , m ∈ Z be rational functions defined by x m−1 x m+1 = x b m +1 if m is odd and x m−1 x m+1 = x c m +1 if m is even. In this short note, we prove that for any m, k ∈ Z, x k can be expressed as a substraction-free Laurent polynomial in Z[x ±1 m , x ±1 m+1 ]. This proves(More)
We study cluster algebras associated to a quiver equipped with a group of admissible automorphisms. This enables us to realize cluster algebras of non simply laced types as quotients of cluster algebras of simply laced types. We then generalize well known results on cluster algebras as denominators theorems and, under some conditions, the linear(More)
Progress in Computational Fluid Dynamics (CFD) methods holds potential for the advancement of wind energy resource assessment in complex urban terrain by modeling wind circulation around urban obstacles. The geometry in urban areas is significantly more complex than for open rural spaces and has a critical influence on wind flow at the micro-meteorological(More)
BACKGROUND Transcranial color duplex ultrasound (TCCD) is becoming an important tool for cerebral monitoring of brain-injured patients. To date, TCCD reproducibility has been studied in healthy volunteers or patients with subarachnoid hemorrhage and its efficiency in many brain injuries has not been proved. Our aim was to evaluate TCCD interobserver(More)
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